Discussion
A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:
Answer: B
The maximum stress occurs only at the bottom fibres.
In pure bending, normal stress is \(\sigma = My/I\), proportional to the distance y from the neutral axis, which passes through the centroid. A T-section is symmetric only about the vertical axis. Its wide flange is at the top, which pulls the centroid up toward the flange, so the bottom of the web is farther from the neutral axis than the top of the flange. The largest |y|, and so the largest stress, is at the bottom fibres.
Equal stresses at top and bottom would need a section symmetric about the horizontal axis, such as an I or a rectangle. At the centroidal fibres y = 0, so the bending stress there is zero, the smallest, not the largest.
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